Question
In: Statistics and Probability
There are 5 faculty, 4 students, and 3 office staff eligible to serve on a 6-person...
There are 5 faculty, 4 students, and 3 office staff eligible to serve on a 6-person committee. How many committees are possible containing at most 1 faculty member?
- A. 112
- B. 105
- C. 277,200
- D. 12,600
- E. 12
- F. 2310
Solutions
Expert Solution
Number of faculty member = 5
Number of students and office staff = 4+3 = 7
Number of committees possible to be formed with 1 faculty member
= 7C5 
5C1 = 21
5 = 105
Number of committees possible to be formed with no faculty member = 7C6 = 7
Number of committees possible to be formed containing at most 1 faculty member = (Number of committees possible to be formed with 1 faculty member + Number of committees possible to be formed with no faculty member)
Number of committees possible to be formed containing at most 1 faculty member = (105 + 7) = 112
Answer: A. 112
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